Finite Size Analysis of Luttinger Liquids with a source of 2k_f Scattering

TL;DR

This paper analyzes the finite size spectrum of Luttinger liquids with 2k_f scattering, identifying irrelevant operators and their effects on transport and conductance.

Contribution

It provides a numerical analysis confirming two irrelevant operators and details their influence on transport properties in finite Luttinger liquids.

Findings

Existence of two irrelevant operators: particle hopping and charge oscillations.

Hopping dominates temperature dependence of conductance.

Both operators influence frequency dependence.

Abstract

Numerical analysis of the spectrum of large finite size Luttinger liquids (g<1) in the presence of a single source of 2k_f scattering has been made possible thanks to an effective integration of high degrees of freedom. Presence of irrelevant operators and their manifestation in transport are issues treated independently. We confirm the existence of two irrelevant operators: particle hopping and charge oscillations, with regions of dominance separated by g=1/2. Temperature dependence of conductance is shown to be dominated by hopping alone. Frequency dependence is affected by both irrelevant operators.